In the proof of Theorem REF  we relied on [1]}. However, that work considers a learning problem over a compact convex set, while the dual update to which we apply this result has an unbounded decision space \(\lambda \in \mathbb {R}_+^d\) . This indeed does not pose a problem for our analysis. Firstly, one can see that for the standard FTRL analysis it suffices to have closed sets, see for example [2]}. Secondly, the boundedness of the set is useful when we need to upper-bound the term \(q_{0:T-1}(\lambda )\)  that appears in the RHS of (REF ). In our analysis, this is not necessary as we cancel this term by setting \(\lambda =0\) .
